Borel subrings of the reals

Gerald A. Edgar, Chris Miller

Type: Article

Publication Date: 2002-06-12

Citations: 45

DOI: https://doi.org/10.1090/s0002-9939-02-06653-4

Abstract

A Borel (or even analytic) subring of $\mathbb R$ either has Hausdorff dimension $0$ or is all of $\mathbb R$. Extensions of the method of proof yield (among other things) that any analytic subring of $\mathbb C$ having positive Hausdorff dimension is equal to either $\mathbb R$ or $\mathbb C$.

Locations

Proceedings of the American Mathematical Society - View - PDF

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